Binary.com Forex Trading

binary.com Interview Question (lite version answer)

®γσ, Lian Hu 白戸則道®

2017-05-21

1. Introduction

Below are the questionaire. Here I created this file to apply MCMCpack and forecast to compelete the questions prior to completed the Ridge, ElasticNet and LASSO regression (quite alot of models for comparison).

Remarks : Here I try to predict the sell/buy price and also settled price. However just noticed the question asking about prediction of the variance1 The profit is made based on the range of variance Hi-Lo price but not the accuracy of the highest, lowest or closing price. based on mean price. Will conduct another study and answer for the variance.

2. Content

2.1 Question 1

2.1.1 Read Data

## 
## Do not execute...
## 
## Remove all objects include hidden objects.
rm(list = ls(all.names = TRUE))

## get currency dataset online.
getFX('USD/JPY', from = '2014-01-01', to = '2017-01-20')
USDJPY <- xts(USDJPY[, -1], order.by = USDJPY$Date)

## dateID
dateID <- index(USDJPY)
dateID0 <- ymd('2015-01-01')
dateID <- dateID[dateID > dateID0]
obs.data <- USDJPY[index(USDJPY) > dateID0]

## Now we try to use the daily mean value which is (Hi + Lo) / 2.
pred.data <- ldply(dateID, function(dt) {
  smp = USDJPY
  dtr = last(index(smp[index(smp) < dt]))
  smp = smp[paste0(dtr %m-% years(1), '/', dtr)]
  frd = as.numeric(difftime(dt, dtr), units = 'days')
  fit = ets(smp) #https://www.otexts.org/fpp/7/7
  data.frame(Date = dt, forecast(fit, h = frd)) %>% tbl_df
  }, .parallel = FALSE) %>% tbl_df

cmp.data <- xts(pred.data[, -1], order.by = pred.data$Date)
cmp.data <- cbind(cmp.data, obs.data)
rm(obs.data, pred.data)

# Test the models
lm(Point.Forecast~ USD.JPY, data = cmp.data)
MCMCregress(Point.Forecast~ USD.JPY, data = cmp.data)


plot(forecast(fit))
forecast(fit, h = 4)
## Mn(Fund) to retrieve the Mean column.
has.Mn <- function (x, which = FALSE) {
  colAttr <- attr(x, 'Mn')
  if(!is.null(colAttr)) 
    return(if (which) colAttr else TRUE)
  loc <- grep('Mean', colnames(x), ignore.case = TRUE)
  
  if(!identical(loc, integer(0))) {
    return(if (which) loc else TRUE)
  } else FALSE 
  }
  
Mn <- function(x) {
  if(has.Mn(x)) 
    return(x[, grep("Mean", colnames(x), ignore.case = TRUE)])
  stop("subscript out of bounds: no column name containing \"Mean\"")
  }
## get currency dataset online.
## http://stackoverflow.com/questions/24219694/get-symbols-quantmod-ohlc-currency-data
#'@ getFX('USD/JPY', from = '2014-01-01', to = '2017-01-20')

## getFX() doesn't shows Op, Hi, Lo, Cl price but only price. Therefore no idea to place bets.
#'@ USDJPY <- getSymbols('JPY=X', src = 'yahoo', from = '2014-01-01', 
#'@                      to = '2017-01-20', auto.assign = FALSE)
#'@ names(USDJPY) <- str_replace_all(names(USDJPY), 'JPY=X', 'USDJPY')
#'@ USDJPY <- xts(USDJPY[, -1], order.by = USDJPY$Date)

#'@ saveRDS(USDJPY, './data/USDJPY.rds')
USDJPY <- read_rds(path = './data/USDJPY.rds')

2.1.2 ARIMA vs ETS

Below are some articles with regards exponential smoothing.

It is a common myth that ARIMA models are more general than exponential smoothing. While linear exponential smoothing models are all special cases of ARIMA models, the non-linear exponential smoothing models have no equivalent ARIMA counterparts. There are also many ARIMA models that have no exponential smoothing counterparts. In particular, every ETS model2 ets() : Usually a three-character string identifying method using the framework terminology of Hyndman et al. (2002) and Hyndman et al. (2008). The first letter denotes the error type (“A”, “M” or “Z”); the second letter denotes the trend type (“N”,“A”,“M” or “Z”); and the third letter denotes the season type (“N”,“A”,“M” or “Z”). In all cases, “N”=none, “A”=additive, “M”=multiplicative and “Z”=automatically selected. So, for example, “ANN” is simple exponential smoothing with additive errors, “MAM” is multiplicative Holt-Winters’ method with multiplicative errors, and so on. It is also possible for the model to be of class “ets”, and equal to the output from a previous call to ets. In this case, the same model is fitted to y without re-estimating any smoothing parameters. See also the use.initial.values argument. is non-stationary, while ARIMA models can be stationary.

The ETS models with seasonality or non-damped trend or both have two unit roots (i.e., they need two levels of differencing to make them stationary). All other ETS models have one unit root (they need one level of differencing to make them stationary).

The following table gives some equivalence relationships for the two classes of models.

ETS model ARIMA model Parameters
\(ETS(A, N, N)\) \(ARIMA(0, 1, 1)\) \(θ_{1} = α − 1\)
\(ETS(A, A, N)\) \(ARIMA(0, 2, 2)\) \(θ_{1} = α + β − 2\)
\(θ_{2} = 1 − α\)
\(ETS(A, A_{d}, N)\) \(ARIMA(1, 1, 2)\) \(ϕ_{1} = ϕ\)
\(θ_{1} = α + ϕβ − 1 − ϕ\)
\(θ_{2} = (1 − α)ϕ\)
\(ETS(A, N, A)\) \(ARIMA(0, 0, m)(0, 1, 0)_{m}\)
\(ETS(A, A, A)\) \(ARIMA(0, 1, m+1)(0, 1, 0)_{m}\)
\(ETS(A, A_{d}, A)\) \(ARIMA(1, 0, m+1)(0, 1, 0)_{m}\)

For the seasonal models, there are a large number of restrictions on the ARIMA parameters.

Kindly refer to 8.10 ARIMA vs ETS for further details.

## Now we try to use the daily mean value which is (Hi + Lo) / 2.
## Hi for predict daily highest price. (selling daytrade)
## Lo for predict daily lowest price. (buying daytrade)
simPrice <- function(mbase, .prCat = 'Mn', .baseDate = ymd('2015-01-01'), .parallel = FALSE, .model = 'ZZZ') {
  
  if(!is.xts(mbase)) mbase <- xts(mbase[, -1], order.by = mbase$Date)
  
  ## dateID
  dateID <- index(mbase)
  if(!is.Date(.baseDate)) {
    dateID0 <- ymd(.baseDate); rm(.baseDate)
  } else {
    dateID0 <- .baseDate; rm(.baseDate)
  }
  dateID <- dateID[dateID >= dateID0]
  
  ## Set as our daily settlement price.
  obs.data <- mbase[index(mbase) > dateID0]
  price.category <- c('Op', 'Hi', 'Mn', 'Lo', 'Cl')
  
  if(.prCat %in% price.category) {
    if(.prCat == 'Op') {
      obs.data2 <- Op(mbase)
      
    } else if(.prCat == 'Hi') {
      obs.data2 <- Hi(mbase)
      
    } else if(.prCat == 'Mn') { #mean of highest and lowest
      obs.data2 <- cbind(Hi(mbase), Lo(mbase), USDJPY.Md = rowMeans(cbind(Hi(mbase), Lo(mbase))))[,-c(1:2)]
      
    } else if(.prCat == 'Lo') {
      obs.data2 <- Lo(mbase)
      
    } else if(.prCat == 'Cl') {
      obs.data2 <- Cl(mbase)
      
    } else {
      stop('Kindly choose .prCat = "Op", .prCat = "Hi", .prCat = "Mn", .prCat = "Lo" or .prCat = "Cl".')
    }
  } else {
    stop('Kindly choose .prCat = "Op", .prCat = "Hi", .prCat = "Mn", .prCat = "Lo" or .prCat = "Cl".')
  }
  
  pred.data <- ldply(dateID, function(dt) {
      smp = obs.data2
      dtr = last(index(smp[index(smp) < dt]))
      smp = smp[paste0(dtr %m-% years(1), '/', dtr)]
      frd = as.numeric(difftime(dt, dtr), units = 'days')
      fit = ets(smp, model = .model) #exponential smoothing model.
      if(frd > 1) dt = seq(dt - days(frd), dt, by = 'days')[-1]
      data.frame(Date = dt, forecast(fit, h = frd)) %>% tbl_df
    }, .parallel = .parallel) %>% tbl_df

  cmp.data <- xts(pred.data[, -1], order.by = pred.data$Date)
  cmp.data <- cbind(cmp.data, obs.data)
  rm(obs.data, pred.data)
  
  return(cmp.data)
  }
## Sorry ARIMA, but I’m Going Bayesian
## http://multithreaded.stitchfix.com/blog/2016/04/21/forget-arima/
#'@ library('bsts')

## Need to testing and compare the models (packages : MCMCPack and bsts).
## Modelling
fit.op <- simPrice(USDJPY, .prCat = 'Op') #will take a minute
fit.hi <- simPrice(USDJPY, .prCat = 'Hi') #will take a minute
fit.mn <- simPrice(USDJPY, .prCat = 'Mn') #will take a minute
fit.lo <- simPrice(USDJPY, .prCat = 'Lo') #will take a minute
fit.cl <- simPrice(USDJPY, .prCat = 'Cl') #will take a minute

2.1.3 MCMC

Need to refer to MCMC since I am using exponential smoothing models…

## Need to test and read through the MCMCregress... after few months later (when free)... Start working as a servant at Bah-Kut-Teh restorant tommorrow 01-Mar-2017.

## Test the models
## opened price fit data
summary(lm(Point.Forecast~ USDJPY.Close, data = fit.op))
## 
## Call:
## lm(formula = Point.Forecast ~ USDJPY.Close, data = fit.op)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4353 -0.4004 -0.0269  0.3998  3.3978 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.180332   0.490019   0.368    0.713    
## USDJPY.Close 0.998722   0.004256 234.666   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7286 on 533 degrees of freedom
##   (216 observations deleted due to missingness)
## Multiple R-squared:  0.9904, Adjusted R-squared:  0.9904 
## F-statistic: 5.507e+04 on 1 and 533 DF,  p-value: < 2.2e-16
summary(MCMCregress(Point.Forecast~ USDJPY.Close, data = fit.op))
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                Mean       SD  Naive SE Time-series SE
## (Intercept)  0.1808 0.489606 4.896e-03      4.896e-03
## USDJPY.Close 0.9987 0.004257 4.257e-05      4.257e-05
## sigma2       0.5330 0.033014 3.301e-04      3.301e-04
## 
## 2. Quantiles for each variable:
## 
##                 2.5%     25%    50%    75%  97.5%
## (Intercept)  -0.7795 -0.1487 0.1848 0.5094 1.1441
## USDJPY.Close  0.9904  0.9959 0.9987 1.0016 1.0070
## sigma2        0.4716  0.5100 0.5317 0.5549 0.6009
## highest price fit data
summary(lm(Point.Forecast~ USDJPY.Close, data = fit.hi))
## 
## Call:
## lm(formula = Point.Forecast ~ USDJPY.Close, data = fit.hi)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3422 -0.3298 -0.0987  0.2166  3.2868 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.140616   0.379253   3.008  0.00276 ** 
## USDJPY.Close 0.993982   0.003294 301.765  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5639 on 533 degrees of freedom
##   (216 observations deleted due to missingness)
## Multiple R-squared:  0.9942, Adjusted R-squared:  0.9942 
## F-statistic: 9.106e+04 on 1 and 533 DF,  p-value: < 2.2e-16
summary(MCMCregress(Point.Forecast~ USDJPY.Close, data = fit.hi))
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                Mean       SD  Naive SE Time-series SE
## (Intercept)  1.1410 0.378933 3.789e-03      3.789e-03
## USDJPY.Close 0.9940 0.003295 3.295e-05      3.295e-05
## sigma2       0.3193 0.019776 1.978e-04      1.978e-04
## 
## 2. Quantiles for each variable:
## 
##                2.5%    25%    50%    75%  97.5%
## (Intercept)  0.3978 0.8860 1.1441 1.3953 1.8865
## USDJPY.Close 0.9875 0.9918 0.9939 0.9962 1.0004
## sigma2       0.2825 0.3055 0.3185 0.3324 0.3599
## mean price fit data (mean price of daily highest and lowest price)
summary(lm(Point.Forecast~ USDJPY.Close, data = fit.mn))
## 
## Call:
## lm(formula = Point.Forecast ~ USDJPY.Close, data = fit.mn)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.55047 -0.26416 -0.00996  0.26743  1.81654 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.106616   0.326718   0.326    0.744    
## USDJPY.Close 0.999098   0.002838 352.091   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4858 on 533 degrees of freedom
##   (216 observations deleted due to missingness)
## Multiple R-squared:  0.9957, Adjusted R-squared:  0.9957 
## F-statistic: 1.24e+05 on 1 and 533 DF,  p-value: < 2.2e-16
summary(MCMCregress(Point.Forecast~ USDJPY.Close, data = fit.mn))
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                Mean       SD  Naive SE Time-series SE
## (Intercept)  0.1069 0.326443 3.264e-03      3.264e-03
## USDJPY.Close 0.9991 0.002838 2.838e-05      2.838e-05
## sigma2       0.2369 0.014676 1.468e-04      1.468e-04
## 
## 2. Quantiles for each variable:
## 
##                 2.5%     25%    50%    75%  97.5%
## (Intercept)  -0.5333 -0.1127 0.1096 0.3260 0.7492
## USDJPY.Close  0.9935  0.9972 0.9991 1.0010 1.0046
## sigma2        0.2096  0.2267 0.2364 0.2467 0.2671
## lowest price fit data
summary(lm(Point.Forecast~ USDJPY.Close, data = fit.lo))
## 
## Call:
## lm(formula = Point.Forecast ~ USDJPY.Close, data = fit.lo)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1318 -0.2450  0.0860  0.3331  1.4818 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.3885     0.3684  -3.769 0.000182 ***
## USDJPY.Close   1.0083     0.0032 315.094  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5478 on 533 degrees of freedom
##   (216 observations deleted due to missingness)
## Multiple R-squared:  0.9947, Adjusted R-squared:  0.9947 
## F-statistic: 9.928e+04 on 1 and 533 DF,  p-value: < 2.2e-16
summary(MCMCregress(Point.Forecast~ USDJPY.Close, data = fit.lo))
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                 Mean       SD  Naive SE Time-series SE
## (Intercept)  -1.3881 0.368114 3.681e-03      3.681e-03
## USDJPY.Close  1.0082 0.003201 3.201e-05      3.201e-05
## sigma2        0.3013 0.018663 1.866e-04      1.866e-04
## 
## 2. Quantiles for each variable:
## 
##                 2.5%     25%     50%     75%   97.5%
## (Intercept)  -2.1101 -1.6358 -1.3851 -1.1410 -0.6638
## USDJPY.Close  1.0020  1.0061  1.0082  1.0104  1.0145
## sigma2        0.2666  0.2883  0.3006  0.3137  0.3397
## closed price fit data
summary(lm(Point.Forecast~ USDJPY.Close, data = fit.cl))
## 
## Call:
## lm(formula = Point.Forecast ~ USDJPY.Close, data = fit.cl)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4339 -0.4026 -0.0249  0.3998  3.4032 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.17826    0.49050   0.363    0.716    
## USDJPY.Close  0.99873    0.00426 234.437   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7293 on 533 degrees of freedom
##   (216 observations deleted due to missingness)
## Multiple R-squared:  0.9904, Adjusted R-squared:  0.9904 
## F-statistic: 5.496e+04 on 1 and 533 DF,  p-value: < 2.2e-16
summary(MCMCregress(Point.Forecast~ USDJPY.Close, data = fit.cl))
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                Mean       SD  Naive SE Time-series SE
## (Intercept)  0.1787 0.490086 4.901e-03      4.901e-03
## USDJPY.Close 0.9987 0.004261 4.261e-05      4.261e-05
## sigma2       0.5340 0.033079 3.308e-04      3.308e-04
## 
## 2. Quantiles for each variable:
## 
##                 2.5%     25%    50%    75%  97.5%
## (Intercept)  -0.7825 -0.1511 0.1827 0.5077 1.1430
## USDJPY.Close  0.9904  0.9959 0.9987 1.0016 1.0071
## sigma2        0.4725  0.5110 0.5327 0.5559 0.6021

Mean Squared Error

fcdata <- do.call(cbind, list(USDJPY.FPOP.Open = fit.op$Point.Forecast, 
                              USDJPY.FPHI.High = fit.hi$Point.Forecast, 
                              USDJPY.FPMN.Mean = fit.mn$Point.Forecast, 
                              USDJPY.FPLO.Low = fit.lo$Point.Forecast, 
                              USDJPY.FPCL.Close = fit.cl$Point.Forecast, 
                              USDJPY.Open = fit.op$USDJPY.Open, 
                              USDJPY.High = fit.op$USDJPY.High, 
                              USDJPY.Low = fit.op$USDJPY.Low, 
                              USDJPY.Close = fit.op$USDJPY.Close))
fcdata <- na.omit(fcdata)
names(fcdata) <- c('USDJPY.FPOP.Open', 'USDJPY.FPHI.High', 'USDJPY.FPMN.Mean', 
                   'USDJPY.FPLO.Low', 'USDJPY.FPCL.Close', 'USDJPY.Open', 
                   'USDJPY.High', 'USDJPY.Low', 'USDJPY.Close')

## Mean Squared Error : comparison of accuracy
paste('Open = ', mean((fcdata$USDJPY.FPOP.Open - fcdata$USDJPY.Open)^2))
## [1] "Open =  0.524327826450961"
paste('High = ', mean((fcdata$USDJPY.FPHI.High - fcdata$USDJPY.High)^2))
## [1] "High =  0.458369038353778"
paste('Mean = ', mean((fcdata$USDJPY.FPMN.Mean - (fcdata$USDJPY.High + fcdata$USDJPY.Low)/2)^2))
## [1] "Mean =  0.414913471187317"
paste('Low = ', mean((fcdata$USDJPY.FPLO.Low - fcdata$USDJPY.Low)^2))
## [1] "Low =  0.623518861674962"
paste('Close = ', mean((fcdata$USDJPY.FPCL.Close - fcdata$USDJPY.Close)^2))
## [1] "Close =  0.531069865476858"

2.1.4 Data Visualization

Plot graph.

## Plot the models
## opened price fit data
autoplot(forecast(ets(fit.op$Point.Forecast), h = 4), facets = TRUE) + geom_forecast(color='#ffcccc', show.legend=FALSE) + labs(x = 'Day', y = 'Forex Price', "Forecasts from ETS model")

#'@ ggplot(data = pd, aes(x = date, y = observed)) + geom_line(color = 'red') + geom_line(aes(y = fitted), color = "blue") + geom_line(aes(y = forecast)) + geom_ribbon(aes(ymin = lo95, ymax = hi95), alpha = .25) + scale_x_date(name = "Time in Decades") + scale_y_continuous(name = "GDP per capita (current US$)") + theme(axis.text.x = element_text(size = 10), legend.justification=c(0,1), legend.position=c(0,1)) + ggtitle("Arima(0,1,1) Fit and Forecast of GDP per capita for Brazil (1960-2013)") + scale_color_manual(values = c("Blue", "Red"), breaks = c("Fitted", "Data", "Forecast")) + ggsave((filename = "gdp_forecast_ggplot.pdf"), width=330, height=180, units=c("mm"), dpi = 300, limitsize = TRUE)

## highest price fit data
autoplot(forecast(ets(fit.hi$Point.Forecast), h = 4), facets = TRUE) + geom_forecast(color = '#FFCCCC', show.legend = FALSE) + labs(x = 'Day', y = 'Forex Price', 'Forecasts from ETS model')

## mean price fit data (mean price of daily highest and lowest price)
autoplot(forecast(ets(fit.mn$Point.Forecast), h = 4), facets = TRUE) + geom_forecast(color = '#FFCCCC', show.legend = FALSE) + labs(x = 'Day', y = 'Forex Price', 'Forecasts from ETS model')

## lowest price fit data
autoplot(forecast(ets(fit.lo$Point.Forecast), h = 4), facets = TRUE) + geom_forecast(color = '#FFCCCC', show.legend = FALSE) + labs(x = 'Day', y = 'Forex Price', 'Forecasts from ETS model')

## opened price fit data
autoplot(forecast(ets(fit.cl$Point.Forecast), h = 4), facets = TRUE) + geom_forecast(color = '#FFCCCC', show.legend = FALSE) + labs(x = 'Day', y = 'Forex Price', 'Forecasts from ETS model')

source('./function/plotChart2.R', local = TRUE)
suppressAll(rm(fit.op, fit.hi, fit.mn, fit.lo, fit.cl))

plotChart2(fcdata, initialName = 'FP', chart.type = 'FP', graph.title = 'USDJPY')

2.1.5 Staking Model

Staking function. Here I apply Kelly criterion as the betting strategy. I don’t pretend to know the order of price flutuation flow from the Hi-Lo price range, therefore I just using Closing price for settlement while the staking price restricted within the variance (Hi-Lo) to made the transaction stand. The settled price can only be closing price unless staking price is opening price which sellable within the Hi-Lo range.

Due to we cannot know the forecasted sell/buy price and also forecasted closing price which is coming first solely from Hi-Lo data, therefore the Profit&Loss will slidely different (sell/buy price = forecasted sell/buy price).

  • Forecasted profit = edge based on forecasted sell/buy price - forecasted settled price.
  • If the forecasted sell/buy price doesn’t exist within the Hi-Lo price, then the transaction is not stand.
  • If the forecasted settled price does not exist within the Hi-Lo price, then the settled price will be the real closing price.
simStakes <- function(mbase, .prCat = 'Op', .baseDate = ymd('2015-01-01'), .parallel = FALSE, .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = FALSE, .filterBets = FALSE) {
  ## .setPrice need to set by refer to closing price, otherwise the P%L will be wrong due to we unable 
  ##   know the price flow based on Hi-Lo price.
  ## Here I set .setPrice to options as : .setPrice = 'Op', .setPrice = 'Hi', .setPrice = 'Mn', .setPrice = 'Lo', .setPrice = 'Cl', .setPrice = 'FPOP', .setPrice = 'FPHI', .setPrice = 'FPMN', .setPrice = 'FPLO', .setPrice = 'FPCL'.
  ## Kindly set .initialFundSize = 1000 but not .initialFundSize = log(1000) for risk management, .fundLeverageLog = FALSE just do not exp() the log() fund size.
  
  #'@ source('./function/simPrice.R', local = TRUE)
  
  if(!is.numeric(.initialFundSize) & length(.initialFundSize) != 1 & .initialFundSize <= 0) {
    stop('Kindly insert a numeric number as initial fund size.')
  }
  
  if(.fundLeverageLog == TRUE) .initialFundSize = log(.initialFundSize)
  
  .setPriceList <- c('Op', 'Hi', 'Mn', 'Lo', 'Cl', 'FPOP', 'FPHI', 'FPMN', 'FPLO', 'FPCL')
  if(.setPrice %in% .setPriceList) {
    .setPrice <- .setPrice
  } else {
    stop("Kindly set .setPrice among c('Op', 'Hi', 'Mn', 'Lo', 'Cl', 'FPOP', 'FPHI', 'FPMN', 'FPLO', 'FPCL')")
  }
  
  nm <- str_extract_all(names(mbase), '^(.*?)+\\.') %>% unlist %>% unique
  names(mbase) <- str_replace_all(names(mbase), '^(.*?)+\\.', 'USDJPY.')
  
  ## forecast staking price.
  fit1 <- simPrice(mbase, .prCat = .prCat, .baseDate = .baseDate, .parallel = .parallel)
  fit1 <- data.frame(Date = index(fit1), coredata(fit1)) %>% tbl_df
  fit1 <- na.omit(fit1)
  
  ## forecast settlement price.
  fit2 <- simPrice(mbase, .prCat = .setPrice, .baseDate = .baseDate, .parallel = .parallel)
  fit2 <- data.frame(Date = index(fit2), coredata(fit2)) %>% tbl_df
  fit2 <- na.omit(fit2)
  
  ## merge dataset
  fitm <- cbind(fit1, forClose = fit2$Point.Forecast) %>% tbl_df
  
  ## convert to probability.
  fitm %<>% mutate(ProbB = pnorm(Point.Forecast, mean = forClose, sd = sd(forClose)), ProbS = 1 - ProbB) #ProbS = pnorm(Point.Forecast, mean = forClose, sd = sd(forClose), lower.tail = FALSE)
  
  ## staking model and bankroll management.
  ## need to refer to Niko Martinen's fund management formula to maximise the stakes and profit base on Kelly models.
  ## https://github.com/scibrokes/betting-strategy-and-model-validation/blob/master/references/Creating%20a%20Profitable%20Betting%20Strategy%20for%20Football%20by%20Using%20Statistical%20Modelling.pdf
  #.... dynamic staking model need to adjusted based on updated bankroll but not portion of fixed USD100 per bet.
  fitm %<>% mutate(BR = .initialFundSize) %>% 
    #'@ mutate(Return.Back = ifelse(Prob > 0.5, Diff * Back * stakes, 0), 
    #'@        Return.Lay = ifelse(Prob < 0.5, -Diff * Lay * stakes, 0))
    mutate(fB = 2 * ProbB - 1, fS = 2 * ProbS - 1, 
           EUB = ProbB * log(BR * (1 + fB)) + (1 - ProbB) * log(BR * (1 - fB)), 
           EUS = ProbS * log(BR * (1 + fS)) + (1 - ProbS) * log(BR * (1 - fS)), 
           #'@ Edge = ifelse(f > 0, EUB, EUS), #For f > 0 need to buy and f <= 0 need to sell.
           #need to study on the risk management on "predicted profit" and "real profit".
           Edge = ifelse(fB > 0, EUB, ifelse(fS > 0, EUS, 0)), 
           PF = ifelse(Point.Forecast >= USDJPY.Low & 
                         Point.Forecast <= USDJPY.High, 
                       Point.Forecast, 0), #if forecasted place-bet price doesn't existing within Hi-Lo price, then the buying action is not stand. Assume there has no web bandwith delay.
           FC = ifelse(forClose >= USDJPY.Low & forClose <= USDJPY.High, 
                       forClose, USDJPY.Close), #if forecasted settle price doesn't existing within Hi-Lo price, then the closing action at closing price. Assume there has no web bandwith delay.
           #'@ Diff = round(forClose - USDJPY.Close, 2),
           ##forecasted closed price minus real close price.
           
           Buy = ifelse(PF > 0 & FC > PF, 1, 0), ##buy action
           Sell = ifelse(PF > 0 & FC < PF, 1, 0), ##sell action
           BuyS = Edge * Buy * (forClose - PF), 
           SellS = Edge * Sell * (PF - forClose), 
           Profit = BuyS + SellS, Bal = BR + Profit)
    
  #'@ fitm %>% dplyr::select(Point.Forecast, forClose, Prob, BR, f, EU, Edge, PF, FC, Buy, Sell, SP, Bal)
  #'@ fitm %>% dplyr::select(ProbB, ProbS, BR, fB, fS, EUB, EUS, Edge, PF, USDJPY.Open, FC, Buy, Sell, BuyS, SellS, Profit, Bal) %>% filter(PF > 0, FC > 0)
  
  for(i in seq(2, nrow(fitm))) {
    fitm$BR[i] = fitm$Bal[i - 1]
    fitm$fB[i] = 2 * fitm$ProbB[i] - 1
    fitm$fS[i] = 2 * fitm$ProbS[i] - 1
    fitm$EUB[i] = fitm$ProbB[i] * log(fitm$BR[i] * (1 + fitm$fB[i])) + 
        (1 - fitm$ProbB[i]) * log(fitm$BR[i] * (1 - fitm$fB[i]))
    fitm$EUS[i] = fitm$ProbS[i] * log(fitm$BR[i] * (1 + fitm$fS[i])) + 
        (1 - fitm$ProbS[i]) * log(fitm$BR[i] * (1 - fitm$fS[i]))
    fitm$Edge[i] = ifelse(fitm$fB[i] > 0, fitm$EUB[i], 
                   ifelse(fitm$fS[i] > 0, fitm$EUS[i], 0)) #For f > 0 need to buy and f <= 0 need to sell.
        #need to study on the risk management on "predicted profit" and "real profit".
    
    fitm$BuyS[i] = fitm$Edge[i] * fitm$Buy[i] * (fitm$forClose[i] - fitm$PF[i])
    fitm$SellS[i] = fitm$Edge[i] * fitm$Sell[i] * (fitm$PF[i] - fitm$forClose[i])
    fitm$Profit[i] = fitm$BuyS[i] + fitm$SellS[i]
    fitm$Bal[i] = fitm$BR[i] + fitm$Profit[i]
    }; rm(i)
  
  names(mbase) <- str_replace_all(names(mbase), '^(.*?)+\\.', nm)
  
  if(.filterBets == TRUE) {
    fitm %<>% filter(PF > 0, FC > 0)
  }
  
  fitm %<>% mutate(RR = Bal/BR)
  
  ## convert the log leverage value of fund size and profit into normal digital figure with exp().
  if(.fundLeverageLog == TRUE) fitm %<>% mutate(BR = exp(BR), BuyS = exp(BuyS), SellS = exp(SellS), Profit = exp(Profit), Bal = exp(Profit))
  
  return(fitm)
  }
##============================ EVAL = FALSE ================================
## 
## Model 1 without leverage.
## 
## Placed orders - Fund size with log

mbase = USDJPY

fundOPHI <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Hi', .initialFundSize = 1000)
fundHIHI <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Hi', .initialFundSize = 1000)
fundMNHI <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Hi', .initialFundSize = 1000)
fundLOHI <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Hi', .initialFundSize = 1000)
fundCLHI <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Hi', .initialFundSize = 1000)

fundOPMN <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Mn', .initialFundSize = 1000)
fundHIMN <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Mn', .initialFundSize = 1000)
fundMNMN <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Mn', .initialFundSize = 1000)
fundLOMN <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Mn', .initialFundSize = 1000)
fundCLMN <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Mn', .initialFundSize = 1000)

fundOPLO <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Lo', .initialFundSize = 1000)
fundHILO <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Lo', .initialFundSize = 1000)
fundMNLO <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Lo', .initialFundSize = 1000)
fundLOLO <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Lo', .initialFundSize = 1000)
fundCLLO <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Lo', .initialFundSize = 1000)

fundOPCL <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Cl', .initialFundSize = 1000)
fundHICL <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Cl', .initialFundSize = 1000)
fundMNCL <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Cl', .initialFundSize = 1000)
fundLOCL <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Cl', .initialFundSize = 1000)
fundCLCL <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Cl', .initialFundSize = 1000)


## Placed orders - Fund size without log
#'@ fundList <- list(fundOPHI = fundOPHI, fundHIHI = fundHIHI, fundMNHI = fundMNHI, fundLOHI = fundLOHI, fundCLHI = fundCLHI, 
#'@                  fundOPMN = fundOPMN, fundHIMN = fundHIMN, fundMNMN = fundMNMN, fundLOMN = fundLOMN, fundCLMN = fundCLMN, 
#'@                  fundOPLO = fundOPLO, fundHILO = fundHILO, fundMNLO = fundMNLO, fundLOLO = fundLOLO, fundCLLO = fundCLLO, 
#'@                  fundOPCL = fundOPCL, fundHICL = fundHICL, fundMNCL = fundMNCL, fundLOCL = fundLOCL, fundCLCL = fundCLCL)
#'@ 
#'@ ldply(fundList, function(x) { x %>% mutate(StartDate = first(Date), LatestDate = last(Date), InitFund = first(BR), LatestFund = last(Bal), Profit = sum(Profit), RR = LatestFund/InitFund) %>% dplyr::select(StartDate, LatestDate, InitFund, LatestFund, Profit, RR) %>% unique }) %>% tbl_df
## A tibble: 20 × 5
#        .id  StartDate LatestDate  InitFund LatestFund     Profit        RR
#      <chr>     <date>     <date>     <dbl>      <dbl>      <dbl>     <dbl>
#1  fundOPHI 2015-01-02 2017-01-20      1000  326.83685   1326.837  1.326837
#2  fundHIHI 2015-01-02 2017-01-20      1000    0.00000   1000.000  1.000000
#3  fundMNHI 2015-01-02 2017-01-20      1000  152.30210   1152.302  1.152302
#4  fundLOHI 2015-01-02 2017-01-20      1000  816.63808   1816.638  1.816638
#5  fundCLHI 2015-01-02 2017-01-20      1000  323.18564   1323.186  1.323186
#6  fundOPMN 2015-01-02 2017-01-20      1000  246.68001   1246.680  1.246680
#7  fundHIMN 2015-01-02 2017-01-20      1000  384.90915   1384.909  1.384909
#8  fundMNMN 2015-01-02 2017-01-20      1000    0.00000   1000.000  1.000000
#9  fundLOMN 2015-01-02 2017-01-20      1000  529.34170   1529.342  1.529342
#10 fundCLMN 2015-01-02 2017-01-20      1000  221.03926   1221.039  1.221039
#11 fundOPLO 2015-01-02 2017-01-20      1000  268.31155   1268.312  1.268312
#12 fundHILO 2015-01-02 2017-01-20      1000  649.35074   1649.351  1.649351
#13 fundMNLO 2015-01-02 2017-01-20      1000  298.28509   1298.285  1.298285
#14 fundLOLO 2015-01-02 2017-01-20      1000    0.00000   1000.000  1.000000
#15 fundCLLO 2015-01-02 2017-01-20      1000  208.85690   1208.857  1.208857
#16 fundOPCL 2015-01-02 2017-01-20      1000   30.55969   1030.560  1.030560
#17 fundHICL 2015-01-02 2017-01-20      1000  400.59057   1400.591  1.400591
#18 fundMNCL 2015-01-02 2017-01-20      1000  117.96808   1117.968  1.117968
#19 fundLOCL 2015-01-02 2017-01-20      1000  530.68975   1530.690  1.530690
#20 fundCLCL 2015-01-02 2017-01-20      1000    0.00000   1000.000  1.000000
##============================ EVAL = FALSE ================================
## 
## Leveraged model 2
## 
## Placed orders - Fund size with log
fundOPHI <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Hi', .initialFundSize = log(1000))
fundHIHI <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Hi', .initialFundSize = log(1000))
fundMNHI <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Hi', .initialFundSize = log(1000))
fundLOHI <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Hi', .initialFundSize = log(1000))
fundCLHI <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Hi', .initialFundSize = log(1000))

fundOPMN <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Mn', .initialFundSize = log(1000))
fundHIMN <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Mn', .initialFundSize = log(1000))
fundMNMN <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Mn', .initialFundSize = log(1000))
fundLOMN <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Mn', .initialFundSize = log(1000))
fundCLMN <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Mn', .initialFundSize = log(1000))

fundOPLO <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Lo', .initialFundSize = log(1000))
fundHILO <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Lo', .initialFundSize = log(1000))
fundMNLO <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Lo', .initialFundSize = log(1000))
fundLOLO <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Lo', .initialFundSize = log(1000))
fundCLLO <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Lo', .initialFundSize = log(1000))

fundOPCL <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Cl', .initialFundSize = log(1000))
fundHICL <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Cl', .initialFundSize = log(1000))
fundMNCL <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Cl', .initialFundSize = log(1000))
fundLOCL <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Cl', .initialFundSize = log(1000))
fundCLCL <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Cl', .initialFundSize = log(1000))

## Placed orders - Fund size with log
#'@ fundList <- list(fundOPHI = fundOPHI, fundHIHI = fundHIHI, fundMNHI = fundMNHI, fundLOHI = fundLOHI, fundCLHI = fundCLHI, 
#'@                  fundOPMN = fundOPMN, fundHIMN = fundHIMN, fundMNMN = fundMNMN, fundLOMN = fundLOMN, fundCLMN = fundCLMN, 
#'@                  fundOPLO = fundOPLO, fundHILO = fundHILO, fundMNLO = fundMNLO, fundLOLO = fundLOLO, fundCLLO = fundCLLO, 
#'@                  fundOPCL = fundOPCL, fundHICL = fundHICL, fundMNCL = fundMNCL, fundLOCL = fundLOCL, fundCLCL = fundCLCL)
#'@ 
#'@ ldply(fundList, function(x) { x %>% mutate(StartDate = first(Date), LatestDate = last(Date), InitFund = first(BR), LatestFund = last(Bal), Profit = sum(Profit), RR = LatestFund/InitFund) %>% dplyr::select(StartDate, LatestDate, InitFund, LatestFund, Profit, RR) %>% unique }) %>% tbl_df

## A tibble: 20 × 7
#        .id  StartDate LatestDate InitFund LatestFund    Profit        RR
#      <chr>     <date>     <date>    <dbl>      <dbl>     <dbl>     <dbl>
#1  fundOPHI 2015-01-02 2017-01-20 6.907755 201.699419 194.79166 29.198982
#2  fundHIHI 2015-01-02 2017-01-20 6.907755   6.907755   0.00000  1.000000
#3  fundMNHI 2015-01-02 2017-01-20 6.907755  75.593102  68.68535 10.943222
#4  fundLOHI 2015-01-02 2017-01-20 6.907755 592.614380 585.70662 85.789718
#5  fundCLHI 2015-01-02 2017-01-20 6.907755 199.023237 192.11548 28.811565
#6  fundOPMN 2015-01-02 2017-01-20 6.907755 145.334081 138.42633 21.039263
#7  fundHIMN 2015-01-02 2017-01-20 6.907755 245.812470 238.90472 35.585000
#8  fundMNMN 2015-01-02 2017-01-20 6.907755   6.907755   0.00000  1.000000
#9  fundLOMN 2015-01-02 2017-01-20 6.907755 359.728088 352.82033 52.075975
#10 fundCLMN 2015-01-02 2017-01-20 6.907755 127.528193 120.62044 18.461597
#11 fundOPLO 2015-01-02 2017-01-20 6.907755 159.124291 152.21654 23.035600
#12 fundHILO 2015-01-02 2017-01-20 6.907755 452.725480 445.81772 65.538726
#13 fundMNLO 2015-01-02 2017-01-20 6.907755 180.580704 173.67295 26.141734
#14 fundLOLO 2015-01-02 2017-01-20 6.907755   6.907755   0.00000  1.000000
#15 fundCLLO 2015-01-02 2017-01-20 6.907755 117.219609 110.31185 16.969276
#16 fundOPCL 2015-01-02 2017-01-20 6.907755  17.669553  10.76180  2.557930
#17 fundHICL 2015-01-02 2017-01-20 6.907755 256.110890 249.20313 37.075849
#18 fundMNCL 2015-01-02 2017-01-20 6.907755  57.745913  50.83816  8.359577
#19 fundLOCL 2015-01-02 2017-01-20 6.907755 357.560612 350.65286 51.762200
#20 fundCLCL 2015-01-02 2017-01-20 6.907755   6.907755   0.00000  1.000000
##============================ EVAL = FALSE ================================
## 
## Leveraged model 3
## 
## Due to the log(.initialfundSize) generates extremely high return compare to normal figure, I added a new parameter ".fundLeverageLog" which convert the normal fund size value into log into calculation and finally convert back to normal fund size figure."

## Placed orders - Fund size without log but exp() Leveraged.
#'@ fundOPHI <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Hi', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundHIHI <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Hi', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundMNHI <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Hi', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundLOHI <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Hi', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundCLHI <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Hi', .initialFundSize = 1000, .fundLeverageLog = TRUE)

#'@ fundOPMN <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Mn', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundHIMN <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Mn', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundMNMN <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Mn', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundLOMN <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Mn', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundCLMN <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Mn', .initialFundSize = 1000, .fundLeverageLog = TRUE)

#'@ fundOPLO <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Lo', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundHILO <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Lo', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundMNLO <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Lo', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundLOLO <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Lo', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundCLLO <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Lo', .initialFundSize = 1000, .fundLeverageLog = TRUE)

#'@ fundOPCL <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundHICL <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundMNCL <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundLOCL <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = TRUE)
#'@ fundCLCL <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Cl', .initialFundSize = 1000, .fundLeverageLog = TRUE)

## A tibble: 20 × 7
#        .id  StartDate LatestDate InitFund   LatestFund       Profit           RR
#       <chr>     <date>     <date>    <dbl>        <dbl>        <dbl>        <dbl>
# 1  fundOPHI 2015-01-02 2017-01-20     1000 2.096972e+27 7.701648e+03 2.096972e+24
# 2  fundHIHI 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 3  fundMNHI 2015-01-02 2017-01-20     1000 3.900327e+04 1.064366e+03 3.900327e+01
# 4  fundLOHI 2015-01-02 2017-01-20     1000 2.718282e+00 9.620574e+09 2.718282e-03
# 5  fundCLHI 2015-01-02 2017-01-20     1000 6.689430e+23 6.611671e+03 6.689430e+20
# 6  fundOPMN 2015-01-02 2017-01-20     1000 2.454335e+01 1.027528e+03 2.454335e-02
# 7  fundHIMN 2015-01-02 2017-01-20     1000 2.718282e+00 2.628152e+03 2.718282e-03
# 8  fundMNMN 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 9  fundLOMN 2015-01-02 2017-01-20     1000 2.718282e+00 3.916608e+04 2.718282e-03
# 10 fundCLMN 2015-01-02 2017-01-20     1000 1.585667e+01 9.900735e+02 1.585667e-02
# 11 fundOPLO 2015-01-02 2017-01-20     1000 1.152381e+00 3.455387e+03 1.152381e-03
# 12 fundHILO 2015-01-02 2017-01-20     1000 2.718282e+00 1.541190e+06 2.718282e-03
# 13 fundMNLO 2015-01-02 2017-01-20     1000 1.040560e+00 3.434093e+03 1.040560e-03
# 14 fundLOLO 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 15 fundCLLO 2015-01-02 2017-01-20     1000 1.152544e+00 2.646148e+03 1.152544e-03
# 16 fundOPCL 2015-01-02 2017-01-20     1000 2.919029e+00 5.465890e+02 2.919029e-03
# 17 fundHICL 2015-01-02 2017-01-20     1000 2.718282e+00 2.278748e+05 2.718282e-03
# 18 fundMNCL 2015-01-02 2017-01-20     1000 1.034658e+01 9.680842e+02 1.034658e-02
# 19 fundLOCL 2015-01-02 2017-01-20     1000 2.718282e+00 2.407137e+08 2.718282e-03
# 20 fundCLCL 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
##============================ EVAL = FALSE ================================
## 
## Leveraged model 4
## 
## Placed orders - Fund size with log and revert back exp() after calculation.
fundOPHI <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Hi', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundHIHI <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Hi', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundMNHI <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Hi', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundLOHI <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Hi', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundCLHI <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Hi', .initialFundSize = log(1000), .fundLeverageLog = TRUE)

fundOPMN <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Mn', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundHIMN <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Mn', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundMNMN <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Mn', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundLOMN <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Mn', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundCLMN <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Mn', .initialFundSize = log(1000), .fundLeverageLog = TRUE)

fundOPLO <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Lo', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundHILO <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Lo', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundMNLO <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Lo', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundLOLO <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Lo', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundCLLO <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Lo', .initialFundSize = log(1000), .fundLeverageLog = TRUE)

fundOPCL <- simStakes(mbase, .prCat = 'Op', .setPrice = 'Cl', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundHICL <- simStakes(mbase, .prCat = 'Hi', .setPrice = 'Cl', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundMNCL <- simStakes(mbase, .prCat = 'Mn', .setPrice = 'Cl', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundLOCL <- simStakes(mbase, .prCat = 'Lo', .setPrice = 'Cl', .initialFundSize = log(1000), .fundLeverageLog = TRUE)
fundCLCL <- simStakes(mbase, .prCat = 'Cl', .setPrice = 'Cl', .initialFundSize = log(1000), .fundLeverageLog = TRUE)

## Placed orders - Fund size with log
#'@ fundList <- list(fundOPHI = fundOPHI, fundHIHI = fundHIHI, fundMNHI = fundMNHI, fundLOHI = fundLOHI, fundCLHI = fundCLHI, 
#'@                  fundOPMN = fundOPMN, fundHIMN = fundHIMN, fundMNMN = fundMNMN, fundLOMN = fundLOMN, fundCLMN = fundCLMN, 
#'@                  fundOPLO = fundOPLO, fundHILO = fundHILO, fundMNLO = fundMNLO, fundLOLO = fundLOLO, fundCLLO = fundCLLO, 
#'@                  fundOPCL = fundOPCL, fundHICL = fundHICL, fundMNCL = fundMNCL, fundLOCL = fundLOCL, fundCLCL = fundCLCL)
#'@ 
#'@ ldply(fundList, function(x) { x %>% mutate(StartDate = first(Date), LatestDate = last(Date), InitFund = first(BR), LatestFund = last(Bal), Profit = sum(Profit), RR = LatestFund/InitFund) %>% dplyr::select(StartDate, LatestDate, InitFund, LatestFund, Profit, RR) %>% unique }) %>% tbl_df
# ldply(fundList, function(x) { x %>% mutate(StartDate = first(Date), LatestDate = last(Date), InitFund = first(BR), LatestFund = last(Bal), Profit = sum(Profit), RR = LatestFund/InitFund) %>% dplyr::select(StartDate, LatestDate, InitFund, LatestFund, Profit, RR) %>% unique }) %>% tbl_df
# A tibble: 20 × 7
#         .id  StartDate LatestDate InitFund   LatestFund       Profit           RR
#       <chr>     <date>     <date>    <dbl>        <dbl>        <dbl>        <dbl>
# 1  fundOPHI 2015-01-02 2017-01-20 6.907755 7.010568e+24 6.130503e+03 1.014884e+24
# 2  fundHIHI 2015-01-02 2017-01-20 6.907755 2.718282e+00 5.350000e+02 3.935116e-01
# 3  fundMNHI 2015-01-02 2017-01-20 6.907755 2.711146e+00 5.344836e+02 3.924786e-01
# 4  fundLOHI 2015-01-02 2017-01-20 6.907755 2.718282e+00 6.039260e+09 3.935116e-01
# 5  fundCLHI 2015-01-02 2017-01-20 6.907755 5.090087e+21 5.261994e+03 7.368655e+20
# 6  fundOPMN 2015-01-02 2017-01-20 6.907755 2.198185e+01 9.372727e+02 3.182199e+00
# 7  fundHIMN 2015-01-02 2017-01-20 6.907755 2.718282e+00 2.362245e+03 3.935116e-01
# 8  fundMNMN 2015-01-02 2017-01-20 6.907755 2.718282e+00 5.350000e+02 3.935116e-01
# 9  fundLOMN 2015-01-02 2017-01-20 6.907755 2.718282e+00 3.257372e+04 3.935116e-01
# 10 fundCLMN 2015-01-02 2017-01-20 6.907755 1.441047e+01 9.002950e+02 2.086129e+00
# 11 fundOPLO 2015-01-02 2017-01-20 6.907755 1.161927e+00 2.719083e+03 1.682061e-01
# 12 fundHILO 2015-01-02 2017-01-20 6.907755 2.718282e+00 1.202578e+06 3.935116e-01
# 13 fundMNLO 2015-01-02 2017-01-20 6.907755 1.043987e+00 2.932865e+03 1.511326e-01
# 14 fundLOLO 2015-01-02 2017-01-20 6.907755 2.718282e+00 5.350000e+02 3.935116e-01
# 15 fundCLLO 2015-01-02 2017-01-20 6.907755 1.166220e+00 1.999664e+03 1.688276e-01
# 16 fundOPCL 2015-01-02 2017-01-20 6.907755 2.861825e+00 5.414756e+02 4.142917e-01
# 17 fundHICL 2015-01-02 2017-01-20 6.907755 2.718282e+00 1.639176e+05 3.935116e-01
# 18 fundMNCL 2015-01-02 2017-01-20 6.907755 7.550813e+00 7.034814e+02 1.093092e+00
# 19 fundLOCL 2015-01-02 2017-01-20 6.907755 2.718282e+00 1.359407e+08 3.935116e-01
# 20 fundCLCL 2015-01-02 2017-01-20 6.907755 2.718282e+00 5.350000e+02 3.935116e-01

2.1.6 Return of Investment

Profit and Loss

## Profit and Loss.
#'@ cbind(
#'@   OP = df.op %>% dplyr::select(Return.Back, Return.Lay) %>% colSums %>% data.frame, 
#'@   HI = df.hi %>% dplyr::select(Return.Back, Return.Lay) %>% colSums %>% data.frame, 
#'@   MN = df.mn %>% dplyr::select(Return.Back, Return.Lay) %>% colSums %>% data.frame, 
#'@   LO = df.lo %>% dplyr::select(Return.Back, Return.Lay) %>% colSums %>% data.frame, 
#'@   CL = df.cl %>% dplyr::select(Return.Back, Return.Lay) %>% colSums %>% data.frame)

## Placed orders - Fund size with log
fundList <- list(fundOPHI = fundOPHI, fundHIHI = fundHIHI, fundMNHI = fundMNHI, fundLOHI = fundLOHI, fundCLHI = fundCLHI, 
                 fundOPMN = fundOPMN, fundHIMN = fundHIMN, fundMNMN = fundMNMN, fundLOMN = fundLOMN, fundCLMN = fundCLMN, 
                 fundOPLO = fundOPLO, fundHILO = fundHILO, fundMNLO = fundMNLO, fundLOLO = fundLOLO, fundCLLO = fundCLLO, 
                 fundOPCL = fundOPCL, fundHICL = fundHICL, fundMNCL = fundMNCL, fundLOCL = fundLOCL, fundCLCL = fundCLCL)

ldply(fundList, function(x) { x %>% mutate(StartDate = first(Date), LatestDate = last(Date), InitFund = first(BR), LatestFund = last(Bal), Profit = sum(Profit), RR = LatestFund/InitFund) %>% dplyr::select(StartDate, LatestDate, InitFund, LatestFund, Profit, RR) %>% unique }) %>% tbl_df
## # A tibble: 20 亊 7
##         .id  StartDate LatestDate InitFund LatestFund    Profit       RR
##       <chr>     <date>     <date>    <dbl>      <dbl>     <dbl>    <dbl>
## 1  fundOPHI 2015-01-02 2017-01-20     1000   1326.837 326.83685 1.326837
## 2  fundHIHI 2015-01-02 2017-01-20     1000   1000.000   0.00000 1.000000
## 3  fundMNHI 2015-01-02 2017-01-20     1000   1152.302 152.30210 1.152302
## 4  fundLOHI 2015-01-02 2017-01-20     1000   1816.638 816.63808 1.816638
## 5  fundCLHI 2015-01-02 2017-01-20     1000   1323.186 323.18564 1.323186
## 6  fundOPMN 2015-01-02 2017-01-20     1000   1246.680 246.68001 1.246680
## 7  fundHIMN 2015-01-02 2017-01-20     1000   1384.909 384.90915 1.384909
## 8  fundMNMN 2015-01-02 2017-01-20     1000   1000.000   0.00000 1.000000
## 9  fundLOMN 2015-01-02 2017-01-20     1000   1529.342 529.34170 1.529342
## 10 fundCLMN 2015-01-02 2017-01-20     1000   1221.039 221.03926 1.221039
## 11 fundOPLO 2015-01-02 2017-01-20     1000   1268.312 268.31155 1.268312
## 12 fundHILO 2015-01-02 2017-01-20     1000   1649.351 649.35074 1.649351
## 13 fundMNLO 2015-01-02 2017-01-20     1000   1298.285 298.28509 1.298285
## 14 fundLOLO 2015-01-02 2017-01-20     1000   1000.000   0.00000 1.000000
## 15 fundCLLO 2015-01-02 2017-01-20     1000   1208.857 208.85690 1.208857
## 16 fundOPCL 2015-01-02 2017-01-20     1000   1030.560  30.55969 1.030560
## 17 fundHICL 2015-01-02 2017-01-20     1000   1400.591 400.59057 1.400591
## 18 fundMNCL 2015-01-02 2017-01-20     1000   1117.968 117.96808 1.117968
## 19 fundLOCL 2015-01-02 2017-01-20     1000   1530.690 530.68975 1.530690
## 20 fundCLCL 2015-01-02 2017-01-20     1000   1000.000   0.00000 1.000000
## A tibble: 20 × 7
#        .id  StartDate LatestDate InitFund   LatestFund       Profit           RR
#       <chr>     <date>     <date>    <dbl>        <dbl>        <dbl>        <dbl>
# 1  fundOPHI 2015-01-02 2017-01-20     1000 2.096972e+27 7.701648e+03 2.096972e+24
# 2  fundHIHI 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 3  fundMNHI 2015-01-02 2017-01-20     1000 3.900327e+04 1.064366e+03 3.900327e+01
# 4  fundLOHI 2015-01-02 2017-01-20     1000 2.718282e+00 9.620574e+09 2.718282e-03
# 5  fundCLHI 2015-01-02 2017-01-20     1000 6.689430e+23 6.611671e+03 6.689430e+20
# 6  fundOPMN 2015-01-02 2017-01-20     1000 2.454335e+01 1.027528e+03 2.454335e-02
# 7  fundHIMN 2015-01-02 2017-01-20     1000 2.718282e+00 2.628152e+03 2.718282e-03
# 8  fundMNMN 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 9  fundLOMN 2015-01-02 2017-01-20     1000 2.718282e+00 3.916608e+04 2.718282e-03
# 10 fundCLMN 2015-01-02 2017-01-20     1000 1.585667e+01 9.900735e+02 1.585667e-02
# 11 fundOPLO 2015-01-02 2017-01-20     1000 1.152381e+00 3.455387e+03 1.152381e-03
# 12 fundHILO 2015-01-02 2017-01-20     1000 2.718282e+00 1.541190e+06 2.718282e-03
# 13 fundMNLO 2015-01-02 2017-01-20     1000 1.040560e+00 3.434093e+03 1.040560e-03
# 14 fundLOLO 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03
# 15 fundCLLO 2015-01-02 2017-01-20     1000 1.152544e+00 2.646148e+03 1.152544e-03
# 16 fundOPCL 2015-01-02 2017-01-20     1000 2.919029e+00 5.465890e+02 2.919029e-03
# 17 fundHICL 2015-01-02 2017-01-20     1000 2.718282e+00 2.278748e+05 2.718282e-03
# 18 fundMNCL 2015-01-02 2017-01-20     1000 1.034658e+01 9.680842e+02 1.034658e-02
# 19 fundLOCL 2015-01-02 2017-01-20     1000 2.718282e+00 2.407137e+08 2.718282e-03
# 20 fundCLCL 2015-01-02 2017-01-20     1000 2.718282e+00 5.350000e+02 2.718282e-03

llply(fundList, function(x) x[c('BR', 'fB', 'fS', 'EUB', 'EUS', 'Edge', 'PF', 'FC', 'Buy', 'Sell', 'BuyS', 'SellS', 'Profit', 'Bal', 'RR')] %>% filter(PF >0 | FC > 0))
## $fundOPHI
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.007746509 -0.007746509 6.907785 6.907785 6.907785   0.0000
## 2  1000.000 -0.110082616  0.110082616 6.913827 6.913827 6.913827 119.8876
## 3  1007.068 -0.039258154  0.039258154 6.915569 6.915569 6.915569   0.0000
## 4  1007.068  0.003366522 -0.003366522 6.914804 6.914804 6.914804 119.4291
## 5  1007.283 -0.098121256  0.098121256 6.919834 6.919834 6.919834   0.0000
## 6  1007.283 -0.067667134  0.067667134 6.917303 6.917303 6.917303 119.3111
## 7  1011.621 -0.044935421  0.044935421 6.920319 6.920319 6.920319   0.0000
## 8  1011.621 -0.103542601  0.103542601 6.924679 6.924679 6.924679 118.2559
## 9  1018.277 -0.048376831  0.048376831 6.927038 6.927038 6.927038   0.0000
## 10 1018.277  0.011428721 -0.011428721 6.925932 6.925932 6.925932 117.7855
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundHIHI
## # A tibble: 535 亊 15
##       BR    fB    fS      EUB      EUS  Edge       PF       FC   Buy  Sell
##    <dbl> <dbl> <dbl>    <dbl>    <dbl> <dbl>    <dbl>    <dbl> <dbl> <dbl>
## 1   1000     0     0 6.907755 6.907755     0   0.0000 119.8700     0     0
## 2   1000     0     0 6.907755 6.907755     0   0.0000 120.4340     0     0
## 3   1000     0     0 6.907755 6.907755     0   0.0000 119.4250     0     0
## 4   1000     0     0 6.907755 6.907755     0 119.3980 119.3980     0     0
## 5   1000     0     0 6.907755 6.907755     0 119.5863 119.5863     0     0
## 6   1000     0     0 6.907755 6.907755     0   0.0000 119.7920     0     0
## 7   1000     0     0 6.907755 6.907755     0   0.0000 118.2120     0     0
## 8   1000     0     0 6.907755 6.907755     0   0.0000 118.3280     0     0
## 9   1000     0     0 6.907755 6.907755     0   0.0000 117.7950     0     0
## 10  1000     0     0 6.907755 6.907755     0 117.6797 117.6797     0     0
## # ... with 525 more rows, and 5 more variables: BuyS <dbl>, SellS <dbl>,
## #   Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundMNHI
## # A tibble: 535 亊 15
##           BR           fB           fS      EUB      EUS     Edge       PF
##        <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.0000  0.003821349 -0.003821349 6.907763 6.907763 6.907763   0.0000
## 2  1000.0000 -0.047573272  0.047573272 6.908887 6.908887 6.908887 120.4692
## 3   996.9558 -0.079100269  0.079100269 6.907838 6.907838 6.907838   0.0000
## 4   996.9558 -0.051211075  0.051211075 6.906018 6.906018 6.906018 118.9236
## 5  1000.2317 -0.056007009  0.056007009 6.909556 6.909556 6.909556   0.0000
## 6  1000.2317 -0.038230691  0.038230691 6.908718 6.908718 6.908718 119.5842
## 7  1002.6775 -0.102753826  0.102753826 6.915718 6.915718 6.915718 119.2241
## 8   996.0814 -0.070077510  0.070077510 6.906286 6.906286 6.906286 118.5676
## 9   991.5957 -0.065126763  0.065126763 6.901438 6.901438 6.901438   0.0000
## 10  991.5957 -0.113308820  0.113308820 6.905749 6.905749 6.905749 116.6273
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundLOHI
## # A tibble: 535 亊 15
##          BR          fB          fS      EUB      EUS     Edge       PF
##       <dbl>       <dbl>       <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.02343199 -0.02343199 6.908030 6.908030 6.908030   0.0000
## 2  1000.000 -0.11560682  0.11560682 6.914453 6.914453 6.914453 119.8360
## 3  1007.425 -0.12995507  0.12995507 6.923621 6.923621 6.923621   0.0000
## 4  1007.425 -0.07743216  0.07743216 6.918154 6.918154 6.918154 118.6801
## 5  1012.392 -0.09830446  0.09830446 6.924911 6.924911 6.924911   0.0000
## 6  1012.392 -0.08069380  0.08069380 6.923330 6.923330 6.923330 119.1899
## 7  1017.572 -0.15022346  0.15022346 6.936501 6.936501 6.936501 118.7790
## 8  1007.869 -0.11925540  0.11925540 6.922721 6.922721 6.922721 118.1091
## 9  1015.539 -0.10678380  0.10678380 6.928887 6.928887 6.928887 117.7410
## 10 1022.409 -0.16977067  0.16977067 6.944398 6.944398 6.944398   0.0000
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundCLHI
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.007628568 -0.007628568 6.907784 6.907784 6.907784   0.0000
## 2  1000.000 -0.112305972  0.112305972 6.914075 6.914075 6.914075 119.8669
## 3  1007.212 -0.034748669  0.034748669 6.915545 6.915545 6.915545   0.0000
## 4  1007.212  0.004968436 -0.004968436 6.914953 6.914953 6.914953 119.4439
## 5  1007.530 -0.097873082  0.097873082 6.920054 6.920054 6.920054   0.0000
## 6  1007.530 -0.070867097  0.070867097 6.917770 6.917770 6.917770 119.2813
## 7  1012.073 -0.042185896  0.042185896 6.920647 6.920647 6.920647   0.0000
## 8  1012.073 -0.103713569  0.103713569 6.925144 6.925144 6.925144 118.2544
## 9  1018.741 -0.043888865  0.043888865 6.927286 6.927286 6.927286   0.0000
## 10 1018.741  0.013426699 -0.013426699 6.926413 6.926413 6.926413 117.8040
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundOPMN
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.003908171 -0.003908171 6.907763 6.907763 6.907763   0.0000
## 2  1000.000 -0.062495264  0.062495264 6.909709 6.909709 6.909709 119.8876
## 3  1004.019  0.039765939 -0.039765939 6.912557 6.912557 6.912557   0.0000
## 4  1004.019  0.054333121 -0.054333121 6.913243 6.913243 6.913243 119.4291
## 5  1007.514 -0.042113105  0.042113105 6.916128 6.916128 6.916128   0.0000
## 6  1007.514 -0.029368111  0.029368111 6.915672 6.915672 6.915672 119.3111
## 7  1009.402  0.057777002 -0.057777002 6.918784 6.918784 6.918784   0.0000
## 8  1009.402 -0.033510743  0.033510743 6.917675 6.917675 6.917675 118.2559
## 9  1011.558  0.016718446 -0.016718446 6.919387 6.919387 6.919387   0.0000
## 10 1011.558  0.124072746 -0.124072746 6.926964 6.926964 6.926964 117.7855
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundHIMN
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.003804721  0.003804721 6.907763 6.907763 6.907763   0.0000
## 2  1000.000  0.047366510 -0.047366510 6.908877 6.908877 6.908877   0.0000
## 3  1000.000  0.078757201 -0.078757201 6.910860 6.910860 6.910860   0.0000
## 4  1000.000  0.050988544 -0.050988544 6.909056 6.909056 6.909056 119.3980
## 5  1003.277  0.055763702 -0.055763702 6.912583 6.912583 6.912583 119.5863
## 6  1006.864  0.038064463 -0.038064463 6.915320 6.915320 6.915320   0.0000
## 7  1006.864  0.102309175 -0.102309175 6.919839 6.919839 6.919839   0.0000
## 8  1006.864  0.069773361 -0.069773361 6.917032 6.917032 6.917032   0.0000
## 9  1006.864  0.064844001 -0.064844001 6.916700 6.916700 6.916700   0.0000
## 10 1006.864  0.112819083 -0.112819083 6.920973 6.920973 6.920973 117.6797
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundMNMN
## # A tibble: 535 亊 15
##       BR    fB    fS      EUB      EUS  Edge       PF       FC   Buy  Sell
##    <dbl> <dbl> <dbl>    <dbl>    <dbl> <dbl>    <dbl>    <dbl> <dbl> <dbl>
## 1   1000     0     0 6.907755 6.907755     0   0.0000 119.8700     0     0
## 2   1000     0     0 6.907755 6.907755     0 120.4692 120.4692     0     0
## 3   1000     0     0 6.907755 6.907755     0   0.0000 119.4250     0     0
## 4   1000     0     0 6.907755 6.907755     0 118.9236 118.9236     0     0
## 5   1000     0     0 6.907755 6.907755     0   0.0000 119.2890     0     0
## 6   1000     0     0 6.907755 6.907755     0 119.5842 119.5842     0     0
## 7   1000     0     0 6.907755 6.907755     0 119.2241 119.2241     0     0
## 8   1000     0     0 6.907755 6.907755     0 118.5676 118.5676     0     0
## 9   1000     0     0 6.907755 6.907755     0   0.0000 117.7950     0     0
## 10  1000     0     0 6.907755 6.907755     0 116.6273 116.6273     0     0
## # ... with 525 more rows, and 5 more variables: BuyS <dbl>, SellS <dbl>,
## #   Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundLOMN
## # A tibble: 535 亊 15
##          BR          fB          fS      EUB      EUS     Edge       PF
##       <dbl>       <dbl>       <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.01952670 -0.01952670 6.907946 6.907946 6.907946   0.0000
## 2  1000.000 -0.06803250  0.06803250 6.910071 6.910071 6.910071 119.8360
## 3  1004.376 -0.05104664  0.05104664 6.913425 6.913425 6.913425   0.0000
## 4  1004.376 -0.02618864  0.02618864 6.912465 6.912465 6.912465 118.6801
## 5  1006.059 -0.04229664  0.04229664 6.914691 6.914691 6.914691   0.0000
## 6  1006.059 -0.04238127  0.04238127 6.914695 6.914695 6.914695 119.1899
## 7  1008.785 -0.04784473  0.04784473 6.917647 6.917647 6.917647 118.7790
## 8  1011.864 -0.04928814  0.04928814 6.920764 6.920764 6.920764 118.1091
## 9  1015.037 -0.04170399  0.04170399 6.923550 6.923550 6.923550 117.7410
## 10 1017.723 -0.05708155  0.05708155 6.926953 6.926953 6.926953   0.0000
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundCLMN
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.003790739 -0.003790739 6.907762 6.907762 6.907762   0.0000
## 2  1000.000 -0.064723580  0.064723580 6.909851 6.909851 6.909851 119.8669
## 3  1004.162  0.044254405 -0.044254405 6.912889 6.912889 6.912889   0.0000
## 4  1004.162  0.055924278 -0.055924278 6.913474 6.913474 6.913474 119.4439
## 5  1007.760 -0.041864475  0.041864475 6.916362 6.916362 6.916362   0.0000
## 6  1007.760 -0.032563800  0.032563800 6.916016 6.916016 6.916016 119.2813
## 7  1009.854  0.060511114 -0.060511114 6.919393 6.919393 6.919393   0.0000
## 8  1009.854 -0.033682265  0.033682265 6.918129 6.918129 6.918129 118.2544
## 9  1012.021  0.021193104 -0.021193104 6.919929 6.919929 6.919929   0.0000
## 10 1012.021  0.126037785 -0.126037785 6.927669 6.927669 6.927669 117.8040
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundOPLO
## # A tibble: 535 亊 15
##          BR            fB            fS      EUB      EUS     Edge
##       <dbl>         <dbl>         <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.0154694206  0.0154694206 6.907875 6.907875 6.907875
## 2  1000.000  0.0055024196 -0.0055024196 6.907770 6.907770 6.907770
## 3  1000.357  0.0898005337 -0.0898005337 6.912150 6.912150 6.912150
## 4  1000.357  0.0796616632 -0.0796616632 6.911288 6.911288 6.911288
## 5  1005.534  0.0001820308 -0.0001820308 6.913274 6.913274 6.913274
## 6  1005.534  0.0129007562 -0.0129007562 6.913357 6.913357 6.913357
## 7  1006.371  0.1043859330 -0.1043859330 6.919564 6.919564 6.919564
## 8  1006.371  0.0156461385 -0.0156461385 6.914228 6.914228 6.914228
## 9  1007.386  0.0578304554 -0.0578304554 6.916788 6.916788 6.916788
## 10 1007.386  0.1784473815 -0.1784473815 6.931122 6.931122 6.931122
## # ... with 525 more rows, and 9 more variables: PF <dbl>, FC <dbl>,
## #   Buy <dbl>, Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>,
## #   Bal <dbl>, RR <dbl>
## 
## $fundHILO
## # A tibble: 535 亊 15
##          BR          fB          fS      EUB      EUS     Edge       PF
##       <dbl>       <dbl>       <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.02310598  0.02310598 6.908022 6.908022 6.908022   0.0000
## 2  1000.000  0.11400900 -0.11400900 6.914268 6.914268 6.914268   0.0000
## 3  1000.000  0.12816224 -0.12816224 6.915991 6.915991 6.915991   0.0000
## 4  1000.000  0.07635786 -0.07635786 6.910673 6.910673 6.910673 119.3980
## 5  1004.961  0.09694316 -0.09694316 6.917410 6.917410 6.917410 119.5863
## 6  1011.272  0.07957455 -0.07957455 6.922133 6.922133 6.922133   0.0000
## 7  1011.272  0.14815718 -0.14815718 6.929980 6.929980 6.929980   0.0000
## 8  1011.272  0.11760788 -0.11760788 6.925896 6.925896 6.925896   0.0000
## 9  1011.272  0.10530642 -0.10530642 6.924519 6.924519 6.924519   0.0000
## 10 1011.272  0.16744322 -0.16744322 6.933049 6.933049 6.933049 117.6797
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundMNLO
## # A tibble: 535 亊 15
##          BR          fB          fS      EUB      EUS     Edge       PF
##       <dbl>       <dbl>       <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.01933914  0.01933914 6.907942 6.907942 6.907942   0.0000
## 2  1000.000  0.06738044 -0.06738044 6.910027 6.910027 6.910027 120.4692
## 3  1004.376  0.05055688 -0.05055688 6.913400 6.913400 6.913400   0.0000
## 4  1004.376  0.02593713 -0.02593713 6.912458 6.912458 6.912458 118.9236
## 5  1006.059  0.04189066 -0.04189066 6.914674 6.914674 6.914674   0.0000
## 6  1006.059  0.04197447 -0.04197447 6.914677 6.914677 6.914677 119.5842
## 7  1008.785  0.04738561 -0.04738561 6.917625 6.917625 6.917625 119.2241
## 8  1011.864  0.04881520 -0.04881520 6.920741 6.920741 6.920741 118.5676
## 9  1015.037  0.04130368 -0.04130368 6.923534 6.923534 6.923534   0.0000
## 10 1015.037  0.05653407 -0.05653407 6.924279 6.924279 6.924279 116.6273
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundLOLO
## # A tibble: 535 亊 15
##       BR    fB    fS      EUB      EUS  Edge       PF       FC   Buy  Sell
##    <dbl> <dbl> <dbl>    <dbl>    <dbl> <dbl>    <dbl>    <dbl> <dbl> <dbl>
## 1   1000     0     0 6.907755 6.907755     0   0.0000 119.8700     0     0
## 2   1000     0     0 6.907755 6.907755     0 119.8360 119.8360     0     0
## 3   1000     0     0 6.907755 6.907755     0   0.0000 119.4250     0     0
## 4   1000     0     0 6.907755 6.907755     0 118.6801 118.6801     0     0
## 5   1000     0     0 6.907755 6.907755     0   0.0000 119.2890     0     0
## 6   1000     0     0 6.907755 6.907755     0 119.1899 119.1899     0     0
## 7   1000     0     0 6.907755 6.907755     0 118.7790 118.7790     0     0
## 8   1000     0     0 6.907755 6.907755     0 118.1091 118.1091     0     0
## 9   1000     0     0 6.907755 6.907755     0 117.7410 117.7410     0     0
## 10  1000     0     0 6.907755 6.907755     0   0.0000 117.3900     0     0
## # ... with 525 more rows, and 5 more variables: BuyS <dbl>, SellS <dbl>,
## #   Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundCLLO
## # A tibble: 535 亊 15
##          BR            fB            fS      EUB      EUS     Edge
##       <dbl>         <dbl>         <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.0155857038  0.0155857038 6.907877 6.907877 6.907877
## 2  1000.000  0.0032885057 -0.0032885057 6.907761 6.907761 6.907761
## 3  1000.213  0.0942224169 -0.0942224169 6.912414 6.912414 6.912414
## 4  1000.213  0.0812332685 -0.0812332685 6.911272 6.911272 6.911272
## 5  1005.493  0.0004286137 -0.0004286137 6.913233 6.913233 6.913233
## 6  1005.493  0.0097337017 -0.0097337017 6.913280 6.913280 6.913280
## 7  1006.124  0.1070773642 -0.1070773642 6.919605 6.919605 6.919605
## 8  1006.124  0.0154761460 -0.0154761460 6.913981 6.913981 6.913981
## 9  1007.129  0.0622508181 -0.0622508181 6.916798 6.916798 6.916798
## 10 1007.129  0.1803677688 -0.1803677688 6.931214 6.931214 6.931214
## # ... with 525 more rows, and 9 more variables: PF <dbl>, FC <dbl>,
## #   Buy <dbl>, Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>,
## #   Bal <dbl>, RR <dbl>
## 
## $fundOPCL
## # A tibble: 535 亊 15
##          BR            fB            fS      EUB      EUS     Edge
##       <dbl>         <dbl>         <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000  0.0001171625 -0.0001171625 6.907755 6.907755 6.907755
## 2  1000.000  0.0022302643 -0.0022302643 6.907758 6.907758 6.907758
## 3  1000.144 -0.0044843098  0.0044843098 6.907909 6.907909 6.907909
## 4  1000.144 -0.0015912841  0.0015912841 6.907900 6.907900 6.907900
## 5  1000.246 -0.0002484005  0.0002484005 6.908001 6.908001 6.908001
## 6  1000.246  0.0031907134 -0.0031907134 6.908006 6.908006 6.908006
## 7  1000.451 -0.0027353174  0.0027353174 6.908210 6.908210 6.908210
## 8  1000.451  0.0001712781 -0.0001712781 6.908207 6.908207 6.908207
## 9  1000.462 -0.0044655769  0.0044655769 6.908228 6.908228 6.908228
## 10 1000.462 -0.0019849334  0.0019849334 6.908220 6.908220 6.908220
## # ... with 525 more rows, and 9 more variables: PF <dbl>, FC <dbl>,
## #   Buy <dbl>, Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>,
## #   Bal <dbl>, RR <dbl>
## 
## $fundHICL
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.007577851  0.007577851 6.907784 6.907784 6.907784   0.0000
## 2  1000.000  0.111564204 -0.111564204 6.913992 6.913992 6.913992   0.0000
## 3  1000.000  0.034517786 -0.034517786 6.908351 6.908351 6.908351   0.0000
## 4  1000.000 -0.004935404  0.004935404 6.907767 6.907767 6.907767 119.3980
## 5  1000.318  0.097225611 -0.097225611 6.912807 6.912807 6.912807 119.5863
## 6  1006.596  0.070397164 -0.070397164 6.916810 6.916810 6.916810   0.0000
## 7  1006.596  0.041905681 -0.041905681 6.915208 6.915208 6.915208   0.0000
## 8  1006.596  0.103027885 -0.103027885 6.919647 6.919647 6.919647   0.0000
## 9  1006.596  0.043597360 -0.043597360 6.915281 6.915281 6.915281   0.0000
## 10 1006.596 -0.013337439  0.013337439 6.914419 6.914419 6.914419 117.6797
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundMNCL
## # A tibble: 535 亊 15
##          BR           fB           fS      EUB      EUS     Edge       PF
##       <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.000 -0.003781993  0.003781993 6.907762 6.907762 6.907762   0.0000
## 2  1000.000  0.064574574 -0.064574574 6.909842 6.909842 6.909842 120.4692
## 3  1004.162 -0.044152403  0.044152403 6.912884 6.912884 6.912884   0.0000
## 4  1004.162 -0.055795457  0.055795457 6.913466 6.913466 6.913466 118.9236
## 5  1007.760  0.041767972 -0.041767972 6.916358 6.916358 6.916358   0.0000
## 6  1007.760  0.032488709 -0.032488709 6.916013 6.916013 6.916013 119.5842
## 7  1009.854 -0.060371767  0.060371767 6.919385 6.919385 6.919385 119.2241
## 8  1005.958  0.033604597 -0.033604597 6.914260 6.914260 6.914260 118.5676
## 9  1008.124 -0.021144218  0.021144218 6.916070 6.916070 6.916070   0.0000
## 10 1008.124 -0.125749407  0.125749407 6.923774 6.923774 6.923774 116.6273
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundLOCL
## # A tibble: 535 亊 15
##           BR           fB           fS      EUB      EUS     Edge       PF
##        <dbl>        <dbl>        <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
## 1  1000.0000  0.015700571 -0.015700571 6.907879 6.907879 6.907879   0.0000
## 2  1000.0000 -0.003312745  0.003312745 6.907761 6.907761 6.907761 119.8360
## 3  1000.2132 -0.094913656  0.094913656 6.912480 6.912480 6.912480   0.0000
## 4  1000.2132 -0.081829942  0.081829942 6.911320 6.911320 6.911320 118.6801
## 5  1005.4926 -0.000431773  0.000431773 6.913233 6.913233 6.913233   0.0000
## 6  1005.4926 -0.009805445  0.009805445 6.913281 6.913281 6.913281 119.1899
## 7  1006.1243 -0.107861822  0.107861822 6.919689 6.919689 6.919689 118.7790
## 8   999.1479 -0.015590206  0.015590206 6.907024 6.907024 6.907024 118.1091
## 9  1000.1514 -0.062708726  0.062708726 6.909874 6.909874 6.909874 117.7410
## 10 1004.1934 -0.181674125  0.181674125 6.928535 6.928535 6.928535   0.0000
## # ... with 525 more rows, and 8 more variables: FC <dbl>, Buy <dbl>,
## #   Sell <dbl>, BuyS <dbl>, SellS <dbl>, Profit <dbl>, Bal <dbl>, RR <dbl>
## 
## $fundCLCL
## # A tibble: 535 亊 15
##       BR    fB    fS      EUB      EUS  Edge       PF       FC   Buy  Sell
##    <dbl> <dbl> <dbl>    <dbl>    <dbl> <dbl>    <dbl>    <dbl> <dbl> <dbl>
## 1   1000     0     0 6.907755 6.907755     0   0.0000 119.8700     0     0
## 2   1000     0     0 6.907755 6.907755     0 119.8669 119.8669     0     0
## 3   1000     0     0 6.907755 6.907755     0   0.0000 119.4250     0     0
## 4   1000     0     0 6.907755 6.907755     0 119.4439 119.4439     0     0
## 5   1000     0     0 6.907755 6.907755     0   0.0000 119.2890     0     0
## 6   1000     0     0 6.907755 6.907755     0 119.2813 119.2813     0     0
## 7   1000     0     0 6.907755 6.907755     0   0.0000 118.2120     0     0
## 8   1000     0     0 6.907755 6.907755     0 118.2544 118.2544     0     0
## 9   1000     0     0 6.907755 6.907755     0   0.0000 117.7950     0     0
## 10  1000     0     0 6.907755 6.907755     0 117.8040 117.8040     0     0
## # ... with 525 more rows, and 5 more variables: BuyS <dbl>, SellS <dbl>,
## #   Profit <dbl>, Bal <dbl>, RR <dbl>

2.1.7 Return of Investment Optimization

## optimise the stakes.
#'@ log(balance + portion Kelly edge ratio)

2.2 Question 2

When I .

2.3 Question 3

3. Conclusion

4. Appendix

4.1 Documenting File Creation

It’s useful to record some information about how your file was created.

[1] “2017-05-21 19:33:20 JST”

4.2 Reference

  1. Stock Market Forecasting Using LASSO Linear Regression Model
  2. Using LASSO from lars (or glmnet) package in R for variable selection
  3. Difference between glmnet() and cv.glmnet() in R?
  4. Testing Kelly Criterion and Optimal f in R
  5. Portfolio Optimization and Monte Carlo Simulation
  6. Glmnet Vignette
  7. lasso怎么用算法实现？
  8. The Sparse Matrix and {glmnet}
  9. Regularization and Variable Selection via the Elastic Net
  10. LASSO, Ridge, and Elastic Net
  11. 热门数据挖掘模型应用入门（一）: LASSO回归
  12. The Lasso Page
  13. Call_Valuation.R
  14. Lecture 6 – Stochastic Processes and Monte Carlo
  15. The caret Package
  16. Time Series Cross Validation
  17. Character-Code.com
  18. Size Matters – Kelly Optimization

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